Problem: As you very well know, this year's funkiest numbers are so called triangular numbers (that is, integers that are representable as <image>, where k is some positive integer), and the coolest numbers are those that are representable as a sum of two triangular numbers.

A well-known hipster Andrew adores everything funky and cool but unfortunately, he isn't good at maths. Given number n, help him define whether this number can be represented by a sum of two triangular numbers (not necessarily different)!

Input

The first input line contains an integer n (1 ≤ n ≤ 109).

Output

Print "YES" (without the quotes), if n can be represented as a sum of two triangular numbers, otherwise print "NO" (without the quotes).

Examples

Input

256


Output

YES


Input

512


Output

NO

Note

In the first sample number <image>.

In the second sample number 512 can not be represented as a sum of two triangular numbers.

Solution (in PYTHON3):

Solution:
import math

n = int(input())
upperBound = int(math.sqrt(2 * n))
funky = []

for i in range (upperBound + 1):
    temp = int(i * (i + 1) / 2)
    funky.append(temp)

flag = False
lower_index = 1
upper_index = upperBound


while(lower_index <= upper_index):
    temp = funky[lower_index] + funky[upper_index] 
    if(temp == n):
        flag = True
        break
    elif(temp < n):
        lower_index+=1
    elif(temp > n):
        upper_index-=1

print("YES") if flag else print("NO")